Determine the maximum bending moment, Mechanical Engineering

Determine the maximum bending moment:

A 12 m span simply supported beam is carrying a consistently distributed load of 2 kN/m over a length of 6 m from the left end and point loads 6 kN, 3 kN and 4 kN at distances of 7 m, 8 m and 9 m, respectively. Draw BM diagram and SF diagram for the beam and determine the maximum bending moment.

2454_Determine the maximum bending moment.png

Figure

Solution

Taking moments around A, and equating to zero.

RB × 12 - (4 × 9) - (3 × 8) - (6 × 7) - 2 × 6 ×(6/2)   = 0

Therefore,        RB = 11.5 kN, and

RA = (2 × 6) + 6 + 3 + 4 - RB = 25 - 11.5 = 13.5 kN

Shear Force (beginning from the left end)

 SF at A, FA = + 13.5 kN

SF at C, FC = + 13.5 - 2 × 6 = + 1.5 kN

SF just left of   D = + 1.5 kN

 SF just right of D = + 1.5 - 6 = - 4.5 kN

SF just left of  E = - 4.5 kN

SF just right of E = - 4.5 - 3 = - 7.5 kN

 SF just left of   F = - 7.5 kN

SF just right of F = - 7.5 - 4 = - 11.5 kN

SF just left of   B = - 11.5 kN = Reaction at B.

Bending Moment

BM at A, MA = 0

BM at C, M  = (13.5 × 6) - 2 × (6 ×(6/2))   = 45 kNm (considering left side)

BM at D, MD = (11.5× 5) - (4 × 2) - (3 × 1) = 46.5 kN m (considering right side)

BM at E,

ME = (11.5 × 4) - (4 × 1) = 42 kN m

BM at F,

MF = (11.5 × 3) = 34.5 kN m

The maximum bending moment take place at D where the shear force changes sign.

                       Mmax = 46.5 kN m.

Posted Date: 1/22/2013 12:44:01 AM | Location : United States







Related Discussions:- Determine the maximum bending moment, Assignment Help, Ask Question on Determine the maximum bending moment, Get Answer, Expert's Help, Determine the maximum bending moment Discussions

Write discussion on Determine the maximum bending moment
Your posts are moderated
Related Questions
Forecasting: Forecasts play a vital role in determining material needs that constitute inventories and in establishing production plans. In this unit, you have studied the imp

(a) Differentiate between carnot Heat pump and carnot Heat engine. What is the basic cycle for a carnot Heat pump ? Explain it. (b) A reversible heat engine delivers 0.6 K at po

how will you apply principle of superposition in a stepped bar?

Remove clutch cover and check clutch operating arm, spring and clutch lifter rod :Check for free movement of rod clutch lifter in the cover right crankcase. Check for lever comple


Define density and specific volume. DENSITY (ρ) Density is illustrated as mass per unit volume; Density = mass/ volume; ρ = m/v, kg/m 3 P for Hg = 13.6 × 10 3 kg/m 3

The resultant of four vertical forces is a couple moment 30 Nm acting counter clockwise. Three of the four forces are shown in fig given below. Evaluate the fourth force.

Centrifugal air compressor: A centrifugal air compressor delivers 15Kg of air per minute. The outlet and inlet conditions are At inlet: Velocity = 5m/sec, enthalpy = 5KJ

Illustrate the assumptions made in Euler's theory. Determine the expression for crippling load for a long column when one end of the column is fixed and other end is hinged.

Explain Rake angle - Angles of a drill It is also known as helix angle .It is the angle formed between a plane containing the drill axis and the leading edge of the land. It c